William thought it would be nice to include $\frac{3}{10}$ of a pound of chocolate in each of the holiday gift bags he made for his friends and family. How many holiday gift bags could William make with $\frac{3}{5}$ of a pound of chocolate?
Solution: To find out how many gift bags William could create, divide the total chocolate ( $\frac{3}{5}$ of a pound) by the amount he wanted to include in each gift bag ( $\frac{3}{10}$ of a pound). $ \dfrac{{\dfrac{3}{5} \text{ pound of chocolate}}} {{\dfrac{3}{10} \text{ pound per bag}}} = {\text{ number of bags}} $ Dividing by a fraction is the same as multiplying by the reciprocal. The reciprocal of ${\dfrac{3}{10} \text{ pound per bag}}$ is ${\dfrac{10}{3} \text{ bags per pound}}$ $ {\dfrac{3}{5}\text{ pound}} \times {\dfrac{10}{3} \text{ bags per pound}} = {\text{ number of bags}} $ $ \dfrac{{3} \cdot {10}} {{5} \cdot {3}} = {\text{ number of bags}} $ Reduce terms with common factors by dividing the $3$ in the numerator and the $3$ in the denominator by $3$ $ \dfrac{{\cancel{3}^{1}} \cdot {10}} {{5} \cdot {\cancel{3}^{1}}} = {\text{ number of bags}} $ Reduce terms with common factors by dividing the $10$ in the numerator and the $5$ in the denominator by $5$ $ \dfrac{{1} \cdot {\cancel{10}^{2}}} {{\cancel{5}^{1}} \cdot {1}} = {\text{ number of bags}} $ Simplify: $ \dfrac{{1} \cdot {2}} {{1} \cdot {1}} = {2} $ William could create 2 gift bags.